How Do You Calculate the Average Density of a Star?

[coffeem]

Determine the average density in solar units of a 0.5 solar mass star with effective temperature 20000K and luminosity 0.03 solar luminosity.

I don't know what the relationship is that I have to use, I have tried using this:

rho = 3m/(4pir^3)

and mixing it with other equation but I have been unable to get a solution? Can someone please tell me what equation I need to know? thanks

 

[mgb_phys]

You need to work out the radius of the star from it's brightness and temperature.
Then with the mass and the equation for the volume of a sphere you can get it's density.

 

[coffeem]

So am I on the right lines if I use: L = wpir^2stefbconsT^4 and dm - pho4pir^2dr? thanks

 

[coffeem]

Hey I have a problem. When I plug the numbers into this I get 1.5ee11 but the answers says it should be 1.5ee5, where could i be getting 6 orders of magnitude from? thanks

 

[mgb_phys]

The luminosity of a black body is L ≈ σT⁴ W m^-2 (σ = 5.67 × 10^-8 W m^-2 K^-4)
The surface area of a sphere is 4π r²
So L ≈ 4π r² σ T⁴

Did you remember to convert to SI units?
0.03 solar luminosity = 0.03 * 3.839 × 10^26 = 1.1517 × 10^25 W
1.1517 × 10²⁵ = 4π r² * 5.67 × 10^-8 * 20,000⁴
1.27 × 10^15 = 4π r²
r = 10^6m ( The suns radius is around 10^9m so this seems reasonable )

 

[coffeem]

The luminosity of a black body is L ≈ σT⁴ W m^-2 (σ = 5.67 × 10^-8 W m^-2 K^-4)
The surface area of a sphere is 4π r²

So L ≈ 4π r² σ T⁴

Hi I was using this. Sorry for my typo above. However when I try and calculate the average density I get the wrong answer. What do you get if you compute it? thanks

 

[mgb_phys]

Mass is 0.5 * sun = 10^30kg
Radius is = 10^6m
Volume of a sphere = 4/3 π r³

Note that this is a white dwarf mostly made of degnerate matter so you might get a rather surprising answer for the density!

 

[coffeem]

Thanks very much that was really helpful. I think I can understand what is going on now.